A shop sells pens, notebooks and files at Rs. 5, Rs. 20 and Rs. 15 each respectively. On Monday it sold 10 pens, 8 notebooks and 5 files, and on Tuesday it sold 6 pens, 12 notebooks and 4 files. Using matrix multiplication, the total sales amount of the shop for the two days is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs. 615
Let the rows of the quantity matrix be the two days and the price matrix be a column:
\( \displaystyle Q = \begin{bmatrix}10&8&5\\6&12&4\end{bmatrix},\quad P = \begin{bmatrix}5\\20\\15\end{bmatrix} \)
The product QP gives the sales amount of each day:
\( \displaystyle QP = \begin{bmatrix}50 + 160 + 75\\30 + 240 + 60\end{bmatrix} = \begin{bmatrix}285\\330\end{bmatrix} \)
So Monday gives Rs. 285 and Tuesday gives Rs. 330. The total is
\(285 + 330 = 615\)
The total sales amount is Rs. 615.